Eric receives a portion of his income from his holdings of Interest-bearing U.S.

Question

Eric receives a portion of his income from his holdings of Interest-bearing U.S. government bonds. The bonds offer a real interest rate of 3.0% per year. The nominal interest rate on the bonds adjusts automatically to the inflation rate. Suppose the government taxes nominal interest income at a rate of 10%. The following table shows two scenarios, a low-Inflation scenario and a high-inflation scenario. Given the real Interest rate of 3.0% per year, find the nominal Interest rate on Eric's bonds, the after-tax nominal Interest rate, and the after-tax real interest rate under each Inflation scenario. Compared with higher inflation rates, a lower inflation rate will the after-tax real interest rate when the government taxes nominal Interest income. This tends saving, thereby the quantity of investment in the economy and the economy's long-run growth rate.

Explanation / Answer

In a scenario of lower rate of inflation:

Inflation rate = 3%

Real interest rate = 3%

Nominal interest rate = real interest rate + inflation = 3% + 3% = 6%     (fisher equation)

After tax nominal interest rate = 6% *(1-tax rate) = 6%*(1-10%) = 5.4%

After tax real interest rate = 6%*(1-10%) – inflation rate = 5.4% - 3% = 2.4%

In a scenario of higher rate of inflation:

Inflation rate = 10%

Real interest rate = 3%

Nominal interest rate = real interest rate + inflation = 10% + 3% = 13%     (fisher equation)

After tax nominal interest rate = 13% *(1-tax rate) = 13%*(1-10%) = 11.7%

After tax real interest rate = 13%*(1-10%) – inflation rate = 11.7% - 10% = 1.7%

Increase / appreciate

Increase the savings

Increasing the quantity of investment

Increase / enhance

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